Geometry, Topology and Physics, Second Edition

By M. Nakahara. 2003

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Classification of topological quantum matter with symmetries (2015, background): “…cutoff term, the net electric current takes the form of Ie ≈ c− e h εF , (3.140) where the integer coefficient is a Z-analytic index that counts the spectral flow (Nakahara, 2003; Volovik, 2003) c− = ( number of forward propagating Dirac modes − number of backward propagating Dirac modes ) .”
Dynamics of filaments and membranes in a viscous fluid (2009, background): “There are useful books with a broader mathematical scope, such as that 2 of (Nakahara, 2003).”
Vortexability: A unifying criterion for ideal fractional Chern insulators (2022, background): “The easiest way to achieve P2 is a magnetic field B 0 ˆ z = ∇× A ext , but experiments have also found strain Landau levels with A el ̸ = 0, A ext = 0 [87]. zero In either case, the number of modes is tied to the number of flux quanta by an index theorem [40] (see e.g. [88] Eq.”
Periodic table for Floquet topological insulators (2016, methodology): “We will need to consider compositions of unitaries, and so, borrowing notation from the composition of paths [48], we write the evolution due to U1 followed by the evolution due to U2 as U1∗U2.”